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Graeme Segal in nLab
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width: 0.3em;"></span> <a href="/nlab/show/HomePage" accesskey="H" title="Home page">Home Page</a> | <a href="/nlab/all_pages" accesskey="A" title="List of all pages">All Pages</a> | <a href="/nlab/latest_revisions" accesskey="U" title="Latest edits and page creations">Latest Revisions</a> | <a href="https://nforum.ncatlab.org/discussion/456/#Item_13" title="Discuss this page in its dedicated thread on the nForum" style="color: black">Discuss this page</a> | <form accept-charset="utf-8" action="/nlab/search" id="navigationSearchForm" method="get"> <fieldset class="search"><input type="text" id="searchField" name="query" value="Search" style="display:inline-block; float: left;" onfocus="this.value == 'Search' ? this.value = '' : true" onblur="this.value == '' ? this.value = 'Search' : true" /></fieldset> </form> <span id='navEnd'></span> </div> <div id="revision"> <html xmlns="http://www.w3.org/1999/xhtml" xmlns:svg="http://www.w3.org/2000/svg" xml:lang="en" lang="en"> <head><meta http-equiv="Content-type" content="application/xhtml+xml;charset=utf-8" /><title>Selected writings</title></head> <body><div style="float:right;margin:0 20px 10px 20px;"><img width="250" src="http://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Graeme_Segal.jpeg/225px-Graeme_Segal.jpeg" alt="Graeme Segal in Berkely, 1982" /><br /> <p><a href="http://commons.wikimedia.org/wiki/File:Graeme_Segal.jpeg">Wikimedia Commons image</a>, taken by</p> <a class="existingWikiWord" href="/nlab/show/George+Bergman">George Bergman</a> <p>in 1982</p> </div> <ul> <li> <p><a href="https://www.maths.ox.ac.uk/people/graeme.segal">institute page</a></p> </li> <li> <p><a href="http://en.wikipedia.org/wiki/Graeme_Segal">Wikipedia entry</a></p> </li> <li> <p><a href="https://www.mathgenealogy.org/id.php?id=27142">MathGenealogy page</a></p> </li> </ul> <h2 id="selected_writings">Selected writings</h2> <p>On <a class="existingWikiWord" href="/nlab/show/classifying+spaces">classifying spaces</a> and <a class="existingWikiWord" href="/nlab/show/spectral+sequences">spectral sequences</a> (and introducing, following <a href="Segal+condition#Grothendieck61">Grothendicek 61</a>, the “<a class="existingWikiWord" href="/nlab/show/Segal+conditions">Segal conditions</a>”, see also at <em><a class="existingWikiWord" href="/nlab/show/complete+Segal+space">complete</a> <a class="existingWikiWord" href="/nlab/show/Segal+space">Segal space</a></em>):</p> <ul> <li id="Segal"><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Classifying spaces and spectral sequences</em>, Inst. Hautes Études Sci. Publ. Math., vol. 34, pp. 105–112 (1968)</li> </ul> <p>On the <a class="existingWikiWord" href="/nlab/show/representation+rings">representation rings</a> of <a class="existingWikiWord" href="/nlab/show/compact+Lie+groups">compact Lie groups</a>:</p> <ul> <li id="Segal68"><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>The representation ring of a compact Lie group</em>, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, January 1968, Volume 34, Issue 1, pp 113-128 (<a href="http://www.numdam.org/item/?id=PMIHES_1968__34__113_0">numdam:PMIHES_1968__34__113_0</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/equivariant+K-theory">equivariant K-theory</a>:</p> <ul> <li id="Segal68"><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Equivariant K-theory</em>, Inst. Hautes Etudes Sci. Publ. Math. <strong>34</strong> (1968) 129-151 [<a href="http://www.numdam.org/item/PMIHES_1968__34__129_0">numdam:PMIHES_1968__34__129_0</a>]</li> </ul> <p>On the <a class="existingWikiWord" href="/nlab/show/Atiyah-Segal+completion+theorem">Atiyah-Segal completion theorem</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Michael+Atiyah">Michael Atiyah</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Equivariant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><mi>K</mi></mrow><annotation encoding="application/x-tex">K</annotation></semantics></math>-theory and completion</em>, J. Differential Geom. Volume 3, Number 1-2 (1969) 1-18 [<a href="http://projecteuclid.org/euclid.jdg/1214428815">euclid:jdg/1214428815</a>]</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/equivariant+stable+homotopy+theory">equivariant stable homotopy theory</a> and the isomorphism between the <a class="existingWikiWord" href="/nlab/show/Burnside+ring">Burnside ring</a> and the <a class="existingWikiWord" href="/nlab/show/equivariant+stable+Cohomotopy">equivariant stable Cohomotopy</a> of the point:</p> <ul> <li id="Segal71"><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Equivariant stable homotopy theory</em>, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, Gauthier-Villars, Paris (1971) 59-63 [<a class="existingWikiWord" href="/nlab/files/SegalEquivariantStableHomotopyTheory.pdf" title="pdf">pdf</a>]</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/configuration+spaces+of+points">configuration spaces of points</a> from <a class="existingWikiWord" href="/nlab/show/iterated+loop+spaces">iterated loop spaces</a>:</p> <ul> <li id="Segal73"><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Configuration-spaces and iterated loop-spaces</em>, Invent. Math. <strong>21</strong> (1973), 213–221. MR 0331377 (<a href="http://dodo.pdmi.ras.ru/~topology/books/segal.pdf">pdf</a>)</li> </ul> <p>On the <a class="existingWikiWord" href="/nlab/show/Kahn-Priddy+theorem">Kahn-Priddy theorem</a> (and a pre-cursor of <a class="existingWikiWord" href="/nlab/show/Snaith%27s+theorem">Snaith's theorem</a>):</p> <ul> <li id="Segal73"><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>The stable homotopy of complex of projective space</em>, The quarterly journal of mathematics (1973) 24 (1): 1-5. (<a class="existingWikiWord" href="/nlab/files/Segal72.pdf" title="pdf">pdf</a>, <a href="https://doi.org/10.1093/qmath/24.1.1">doi:10.1093/qmath/24.1.1</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/K-theory+of+permutative+categories">K-theory of permutative categories</a>, <a class="existingWikiWord" href="/nlab/show/Gamma+spaces">Gamma spaces</a> as models for <a class="existingWikiWord" href="/nlab/show/connective+spectra">connective spectra</a>, and the identification of <a class="existingWikiWord" href="/nlab/show/stable+Cohomotopy">stable Cohomotopy</a> with the <a class="existingWikiWord" href="/nlab/show/K-theory+of+a+permutative+category">K-theory</a> of <a class="existingWikiWord" href="/nlab/show/finite+sets">finite sets</a>:</p> <ul> <li id="Segal74"><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Categories and cohomology theories</em>, Topology vol 13, pp. 293-312, 1974 (<a href="https://doi.org/10.1016/0040-9383(74)90022-6">doi:10.1016/0040-9383(74)90022-6</a>, <a href="http://ncatlab.org/nlab/files/SegalCategoriesAndCohomologyTheories.pdf">pdf</a>)</li> </ul> <p>On the <a class="existingWikiWord" href="/nlab/show/group+completion+theorem">group completion theorem</a>:</p> <ul> <li id="McDuffSegal76"><a class="existingWikiWord" href="/nlab/show/Dusa+McDuff">Dusa McDuff</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Homology fibrations and the “group-completion” theorem</em>, Invent. Math. <strong>31</strong> 3 (1976) 279-284 [<a href="https://doi.org/10.1007/BF01403148">doi:10.1007/BF01403148</a>]</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/equivariant+homotopy+theory">equivariant homotopy theory</a> motivated by equivariant <a class="existingWikiWord" href="/nlab/show/iterated+loop+spaces">iterated loop spaces</a> and <a class="existingWikiWord" href="/nlab/show/configuration+spaces+of+points">configuration spaces of points</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Some results in equivariant homotopy theory</em> (1978) [scan: <a href="https://homepages.warwick.ac.uk/~maaac/segal.html">web</a>, <a class="existingWikiWord" href="/nlab/files/Segal-EquivariantHT.pdf" title="pdf">pdf</a>]</li> </ul> <p>Proving the <a class="existingWikiWord" href="/nlab/show/equivariant+Whitehead+theorem">equivariant Whitehead theorem</a>:</p> <ul> <li id="JamesSegal78"><a class="existingWikiWord" href="/nlab/show/Ioan+James">Ioan James</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, Theorem 1.1 in: <em>On equivariant homotopy type</em>, Topology <strong>17</strong> 3 (1978) 267-272 [<a href="https://doi.org/10.1016/0040-9383(78)90030-7">doi:10.1016/0040-9383(78)90030-7</a>]</li> </ul> <p>On the <a class="existingWikiWord" href="/nlab/show/homotopy+type+of+spaces+of+rational+functions">homotopy type of spaces of rational functions</a> from the <a class="existingWikiWord" href="/nlab/show/Riemann+sphere">Riemann sphere</a> to itself (related to the <a class="existingWikiWord" href="/nlab/show/moduli+space+of+monopoles">moduli space of monopoles</a> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msup><mi>ℝ</mi> <mn>3</mn></msup></mrow><annotation encoding="application/x-tex">\mathbb{R}^3</annotation></semantics></math> and to the <a class="existingWikiWord" href="/nlab/show/configuration+space+of+points">configuration space of points</a> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" class="maruku-mathml"><semantics><mrow><msup><mi>ℝ</mi> <mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\mathbb{R}^2</annotation></semantics></math>):</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>The topology of spaces of rational functions</em>, Acta Math. <strong>143</strong> (1979) 39-72 [<a href="https://projecteuclid.org/euclid.acta/1485890033">euclid:1485890033</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Ralph+L.+Cohen">Ralph L. Cohen</a>, <a class="existingWikiWord" href="/nlab/show/John+D.+S.+Jones">John D. S. Jones</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+B.+Segal">Graeme B. Segal</a>, <em>Stability for holomorphic spheres and Morse theory</em>, in: K. Grove, I. H. Madsen, E. K. Pedersen (eds.) <em>Geometry and Topology: Aarhus</em>, Contemporary Mathematics</p> <p>Volume: 258; (<a href="https://arxiv.org/abs/math/9904185">arXiv:math/9904185</a>, <a href="https://bookstore.ams.org/conm-258">ISBN:978-0-8218-2158-9</a>)</p> </li> </ul> <p>On the <a class="existingWikiWord" href="/nlab/show/ordinary+cohomology">ordinary cohomology</a> of the <a class="existingWikiWord" href="/nlab/show/moduli+space+of+Yang-Mills+monopoles">moduli space of Yang-Mills monopoles</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, Alex Selby, <em>The cohomology of the space of magnetic monopoles</em>, Commun. Math. Phys. 177, 775–787 (1996) (<a href="https://doi.org/10.1007/BF02099547">doi:10.1007/BF02099547</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/equivariant+bundles">equivariant bundles</a> with <a class="existingWikiWord" href="/nlab/show/abelian+group">abelian</a> <a class="existingWikiWord" href="/nlab/show/structure+group">structure group</a>:</p> <ul> <li id="LashofMaySegal83"><a class="existingWikiWord" href="/nlab/show/Richard+Lashof">Richard Lashof</a>, <a class="existingWikiWord" href="/nlab/show/Peter+May">Peter May</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Equivariant bundles with abelian structural group</em>, Contemporary Mathematics <strong>19</strong>, 1983 (<a href="https://doi.org/10.1090/conm/019">doi:10.1090/conm/019</a>, <a href="http://www.math.uchicago.edu/~may/PAPERS/45.pdf">pdf</a>, <a class="existingWikiWord" href="/nlab/files/LashofMaySegalEquivariantBundles.pdf" title="pdf">pdf</a>)</li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/loop+groups">loop groups</a> of <a class="existingWikiWord" href="/nlab/show/compact+Lie+groups">compact Lie groups</a> and their <a class="existingWikiWord" href="/nlab/show/Kac-Moody+group">Kac-Moody group</a> <a class="existingWikiWord" href="/nlab/show/central+extension">central extension</a>:</p> <ul> <li id="PressleySegal"> <p><a class="existingWikiWord" href="/nlab/show/Andrew+Pressley">Andrew Pressley</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Loop groups</em>, Oxford University Press (1988)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Loop groups</em> (<a href="http://people.mpim-bonn.mpg.de/zagier/files/doi/10.1007/BFb0084581/chapter08.pdf">pdf</a>)</p> </li> </ul> <p>On integrable functions in terms of infinitedimensional <a class="existingWikiWord" href="/nlab/show/Sato-Segal-Wilson+Grassmannian">Sato-Segal-Wilson Grassmannian</a></p> <ul> <li>G. Segal, <a class="existingWikiWord" href="/nlab/show/George+Wilson">George Wilson</a>, <em>Loop groups and equations of KdV type</em>, Publ. Math. IHÉS <strong>61</strong>, 5–65 (1985) <a href="http://www.numdam.org/item/PMIHES_1985__61__5_0">numdam</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=87b:58039">MR87b:58039</a> <a href="https://zbmath.org/?q=an:0592.35112">Zbl0592.35112</a></li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/2d+conformal+field+theory">2d conformal field theory</a> and <a class="existingWikiWord" href="/nlab/show/modular+functors">modular functors</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Two-dimensional conformal field theories and modular functors</em>, in: <em>IXth International Congress on Mathematical Physics</em>, Swansea 1988, Adam Hilger, Bristol and New York (1989) 22–37 [<a href="https://dmitripavlov.org/scans/segal-two-dimensional-conformal-field-theories-and-modular-functors.pdf">pdf</a>, <a class="existingWikiWord" href="/nlab/files/Segal-2dCFTandModularFunctors.pdf" title="pdf">pdf</a>]</li> </ul> <p>Further on the <a class="existingWikiWord" href="/nlab/show/FQFT">functorial</a>-definition of <a class="existingWikiWord" href="/nlab/show/2d+conformal+field+theory">2d conformal field theory</a>:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>The definition of conformal field theory</em>, in: K. Bleuler, M. Werner (eds.), <em>Differential geometrical methods in theoretical physics</em> (Proceedings of Research Workshop, Como 1987), NATO Adv. Sci. Inst., Ser. C: Math. Phys. Sci. <strong>250</strong> Kluwer Acad. Publ., Dordrecht (1988) 165-171 [<a href="https://doi.org/10.1007/978-94-015-7809-7">doi:10.1007/978-94-015-7809-7</a>]</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>The definition of conformal field theory</em>, in: <a class="existingWikiWord" href="/nlab/show/Ulrike+Tillmann">Ulrike Tillmann</a> (ed.), <em>Topology, geometry and quantum field theory</em> , London Math. Soc. Lect. Note Ser. <strong>308</strong>, Cambridge University Press (2004) 421-577 [<a href="https://doi.org/10.1017/CBO9780511526398.019">doi:10.1017/CBO9780511526398.019</a>, <a href="https://people.maths.ox.ac.uk/segalg/0521540496txt.pdf">pdf</a>, <a class="existingWikiWord" href="/nlab/files/SegalDefinitionCFT.pdf" title="pdf">pdf</a>]</p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/twisted+K-theory">twisted K-theory</a> and <a class="existingWikiWord" href="/nlab/show/twisted+equivariant+K-theory">twisted equivariant K-theory</a>:</p> <ul> <li id="AtiyahSegal04"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Atiyah">Michael Atiyah</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Twisted K-theory</em>, Ukrainian Math. Bull. <strong>1</strong>, 3 (2004) (<a href="http://arxiv.org/abs/math/0407054">arXiv:math/0407054</a>, <a href="http://iamm.su/en/journals/j879/?VID=10">journal page</a>, <a href="http://iamm.su/upload/iblock/45e/t1-n3-287-330.pdf">published pdf</a>)</p> </li> <li id="AtiyahSegal05"> <p><a class="existingWikiWord" href="/nlab/show/Michael+Atiyah">Michael Atiyah</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Twisted K-theory and cohomology</em> (<a href="http://arxiv.org/abs/math/0510674">arXiv:math/0510674</a>)</p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/quantization">quantization</a> of the <a class="existingWikiWord" href="/nlab/show/electromagnetic+field">electromagnetic field</a> in view of <a class="existingWikiWord" href="/nlab/show/Dirac+charge+quantization">Dirac charge quantization</a> and <a class="existingWikiWord" href="/nlab/show/higher+U%281%29-gauge+theory">higher U(1)-gauge theory</a>:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Daniel+S.+Freed">Daniel S. Freed</a>, <a class="existingWikiWord" href="/nlab/show/Gregory+W.+Moore">Gregory W. Moore</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, p. 7 of: <em>The Uncertainty of Fluxes</em>, Commun. Math. Phys. 271:247-274, 2007 (<a href="https://arxiv.org/abs/hep-th/0605198">arXiv:hep-th/0605198</a>, <a href="https://doi.org/10.1007/s00220-006-0181-3">doi:10.1007/s00220-006-0181-3</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Daniel+Freed">Daniel Freed</a>, <a class="existingWikiWord" href="/nlab/show/Gregory+Moore">Gregory Moore</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Heisenberg Groups and Noncommutative Fluxes</em>, Annals Phys. 322:236-285 (2007) (<a href="http://arxiv.org/abs/hep-th/0605200">arXiv:hep-th/0605200</a>)</p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/Wick+rotation">Wick rotation</a> in <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a> in terms of complex metrics:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Maxim+Kontsevich">Maxim Kontsevich</a>, <a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Wick rotation and the positivity of energy in quantum field theory</em>, The Quarterly Journal of Mathematics <strong>72</strong> 1-2, (2021) 673–699 [<a href="https://arxiv.org/abs/2105.10161">arXiv:2105.10161</a>, <a href="https://doi.org/10.1093/qmath/haab027">doi:10.1093/qmath/haab027</a>]</li> </ul> <p>review talks:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Wick rotation and the positivity of energy in quantum field theory</em>, talk at Institut des Hautes Études Scientifiques (IHÉS), June 2014 (<a href="https://www.youtube.com/watch?feature=player_embedded&v=vTvXHL6ZJik">video recording</a>)</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>, <em>Wick Rotation and the Positivity of Energy in Quantum Field Theory</em>, talk at IAS Physics Group Meeting, December 2021 (<a href="https://www.ias.edu/video/wick-rotation-and-positivity-energy-quantum-field-theory">video recording</a>)</p> </li> </ul> <p>On <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Graeme+Segal">Graeme Segal</a>: <em>A point of view on quantum field theory</em>, lecture series at International Center for Mathematical Sciences (July 2024) [video: <a href="https://youtu.be/iABSxSNBTCk?list=PLUbgZHsSoMEVKB1ePqcmZgoVavZqsAFBj">part 1</a>, <a href="https://youtu.be/a3bni4NiaaI?list=PLUbgZHsSoMEVKB1ePqcmZgoVavZqsAFBj">part 2</a>, <a href="https://youtu.be/pph0hCrIJ4k?list=PLUbgZHsSoMEVKB1ePqcmZgoVavZqsAFBj">part 3</a>, <a href="https://youtu.be/07wUiwEPHwQ?list=PLUbgZHsSoMEVKB1ePqcmZgoVavZqsAFBj">part 4</a>]</li> </ul> <div class="property">category: <a class="category_link" href="/nlab/all_pages/people">people</a></div></body></html> </div> <div class="revisedby"> <p> Last revised on September 13, 2024 at 10:57:40. 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